。
She offered to reissue it.
Literal
She [topic-は] reissue [object-を] offered.
申し出る is a polite, formal verb meaning 'to offer, propose, volunteer (oneself for a task or to provide something).' Built from 申す (humble form of 'say') + 出る ('come out') — literally 'to come forth and humbly say' — it carries an institutional tone, common in business and official contexts. 再発行 ('reissue') is a tight Sino-Japanese compound: 再 ('re-, again') + 発行 ('issue, publish'). Used routinely for replacement documents like cards, certificates, and receipts.